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 A004130 Numerators in expansion of (1-x)^{-1/4}. 5
 1, 1, 5, 15, 195, 663, 4641, 16575, 480675, 1762475, 13042315, 48612265, 729183975, 2748462675, 20809788825, 79077197535, 4823709049635, 18443593425075, 141400882925575, 543277076503525, 8366466978154285, 32270658344309385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Numerators in expansion of sqrt(1/sqrt(1-4x)). - Paul Barry, Jul 12 2005 Denominators are in A088802. - Michael Somos, Aug 23 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA a(n) = prod(k=1, n, (4k-3)/k * 2^A007814(k)), proved by Mitch Harris, following a conjecture by Ralf Stephan. a(n) = 2^(e_2((2n)!)-n)/n! Product[4k+1,{k,0,n-1}], where e_2((2n)!) is the highest power of 2 that divides (2n)! (sequence A005187). - Emanuele Munarini, Jan 25 2011 Numerators in (1-4t)^(-1/4) = 1 + t + (5/2)t^2 + (15/2)t^3 + (195/8)t^4 + (663/8)t^5 + (4641/16)t^6 + (16575/16)t^7 + ... = 1 + t + 5*t^2/2! + 45*t^3/3! + 585*t^4/4! + ... = e.g.f. for the quartic factorials A007696 (cf. A094638). - Tom Copeland, Dec 04 2013 MATHEMATICA Table[Numerator[Binomial[-1/4, n] (-1)^n], {n, 0, 20}] PROG (PARI) {a(n) = if( n<0, 0, numerator( polcoeff( (1 - x +x*O(x^n))^(-1/4), n ) ) ) } /* Michael Somos, Aug 23 2007 */ CROSSREFS Cf. A004134, A004981, A034255, A034385, A048882, A007696, A000265, A049606. Sequence in context: A143048 A261843 A120602 * A088869 A134715 A053918 Adjacent sequences:  A004127 A004128 A004129 * A004131 A004132 A004133 KEYWORD nonn,frac AUTHOR STATUS approved

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Last modified December 6 01:52 EST 2021. Contains 349558 sequences. (Running on oeis4.)